The only consequence is possibly your FC dropping to zero over the winter. Usually when closing, the FC is brought to shock levels (based on your CYA) and then when you cover the pool, you're likely to have some FC left in the pool even by spring if you close late enough with water temps well below 60 degrees. If you do not use a cover, your FC will likely be consumed by sunlight before spring. If you open early enough, this may not be an issue. When your FC drops to zero however, there is a greater chance, but still a small chance, that your CYA will be converted to ammonia by bacteria. This conversion is dependent on low or very little FC and your pool being exposed to a certain strain of soil bacteria. If the conversion were to occur, you'd lose your CYA over the winter and you'd have a very large chlorine demand in the spring to oxidize all the ammonia that was produced. That is unless the ammonia is fully oxidized and outgassed as nitrogen before spring. It's a very complicated process that is still a bit of a mystery to even folks here at TFP but there is a chance of it happening under the right (aka wrong) conditions.
Short story: If you close late and open early, you'll probably still be OK.